Title: Hodge symmetries of singular varieties.Abstract: The Hodge diamond of a smooth projective complex variety exhibits fundamental symmetries, arising from Poincaré duality and the purity of Hodge structures. In the case of a singular projective variety, the complexity of the singularities is closely related to the symmetries of the analogous Hodge–Du Bois diamond. For example, the failure […]

Title: Stable maps to quotient stacks with a properly stable point.Abstract: I will present a compactification of the moduli space of maps from families of curves, to certain moduli spaces M, via the example of M being the GIT moduli space of binary forms of degree 2n. The main application of our results is the construction of […]

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